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Unformatted text preview: MATH 191, Sections 1 and 3 Calculus I Fall 2007 Section 3.2: The Product and Quotient Rules Lets continue amassing shortcuts for computing derivatives. Weve now got rules for differentiating powers, as well as constant multiples, sums, and dif- ferences of functions whose derivatives we already know. We even know the derivative of an exponential function f ( x ) = e x ! Whats missing? Well, lots. Products, for one. Lets examine d dx ( f g ), and see if we can get a nice formula. Sadly, its not what we might immediately expect. First, a motivating Example. Consider the numbers 4 and 7, whose product is 4 7 = 28. What happens if we add a very small quantity, say 1 , to 4, and another small quan- tity, 2 , to 7, and then recompute the product? We now get (4 + 1 )(7 + 2 ) = . This expression represents the value to which the product 4 7 has been changed corresponding to a small change in those values. Whats most interesting here are those two cross-terms in the middle. If we think of 4 and 7 as the valuesare those two cross-terms in the middle....
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